Just to amplify on my previous answer, you can actually have six PWM outputs if you are prepared to sacrifice flexibility of choice of frequency. If you are prepared to accept the "top" as being 256 (0xFF since it is zero-relative) then you can use both "sides" of the counter for PWM output (with different duty cycles).
Since you are committed to a count of 256 then the maximum frequency will be:
1 / (62.5e-9 * 256) / 2 = 31250
That is 31.25 KHz in phase-correct mode, or double that (62.5 KHz) in fast PWM mode. That is probably where you heard of a maximum of 62 KHz.
So it's all about choice. You choose if you want 3 outputs or 6, and you choose if you want a high PWM frequency, or a fine resolution of duty cycle.
Also if you use Timer 1 you have more resolution up your sleeve because that can count up to 16 bits, not 8.